Harv,
In my last mention of Chaitin, a response to Alexander's view that math is fundamental to the universe, I said that Chaitin is suggesting that rational math as needed for the laws of physics are only tiny islands in the sea of irrational math. Perhaps previously I had used the word randomness.
My guess is that the terms rational/irrational are probably even further from the core of Chaitin's suggestions than randomness. I bow to your superior knowledge on this subject. I have only trained in applied math and have not been to concerned with terminology, especially working on Star Wars govt work, you know.
Actually in defining randomness in the above post you taught me more about it than I had previously known. My appreciation had been at the level of if the formula works(gives me the answer I want) use it.
The written material I read about Chaitin's work used the word randomness, probably by mistake, or to reach the average reader. Thinking of the sea as irreducible is much, much more interesting to me. Since his work follows on Goedel's, it's logical that he  Chaitin is talking about solution space that cannot be derived from a finite number of axioms. Thinking back on his mega and supermega numbers it all makes sense if he meant irreducibility.
I cannot remember if you are partial to spiritual or supernatural thinking, but my intuition is that the sea of irreducibility is important to communication in that realm.
BTW, in my response to Alexander I proposed that if all in the universe does come from mathematics; and since there seems to be much, much more math, reducible math, available than has ever been used in the laws of physics, or chemistry and economics for that matter; plus according to Chaitin the availible reducible math solutions are just islands in a sea of irreducible math solutions; then some agency had to be available to pick and choose the particuliar math appropriate for this universe.
If math alone were fundamental, then all the availible math would be used. But since such a tiny fraction of it is actually used in physical laws, we need in addition a selection process.
That need not be God, as many are wont to suggest. It could be the evolution of universes as hypothesized by Smolin.
Smolin suggests that baby universes are produced in black holes. Greene's book "The Elegant Universe" suggests a mechanism without mentioning Smolin Both from Harvard you know Harv.
Therefore universes with the optimum math and physical parameters to generate the greatest number of black holes will tend to dominate the infinite nice name for the infinite collection of universes. Since we have a black hole in every galaxy, we are probably in an optimum universe. Assuming that there exists some form of universe destruction, perhaps overexpansion into nothingness, then an infinite amount of time having elapsed, only optimum universes are now likely. So evolution selects the math.
But just like evolution of life on earth, it could be a guided evolution. Anyway, that's my belief. No bottomline, except a thank you for opening my eyes even wider.
